How to Sketch the Graph of Square Root Functions, ( f(x)=√ x )

By Zadock Reid; Updated April 24, 2017

This Article will show how to Sketch the graphs of Square Root Function by using only three different values for ' x ',then finding the Points through which the graph of the Equations/Functions are drawn, also it will show how the Graphs Vertically Translates ( moves up or down ), Horizontally Translates ( moves to the left or to the right ), and how the Graph simultaneously does Both Translations.

The Equation of a Square Root Function has the Form,... y = f(x) = A√x ,where ( A ) must not be equal to zero ( 0 ).If ( A ) is greater than Zero ( 0 ), that is ( A ) is a Positive Number, then The Shape of the Graph of the Square Root Function is similar to the Upper Half of the letter,' C '. If ( A ) is Less than Zero ( 0 ), that is ( A ) is a Negative Number, the Shape of the Graph is similar to that of the Lower Half of the letter ' C '. Please Click on the Image for a better view.

Given y = f(x) = A√x, where ( A ) is a Real Number and ( A ) not equal to Zero ( 0 ), and substituting, x = ( -1 ) into the Equation we get y = f(-1) = A√(-1) = i ( which is an imaginary number). So the First Point has no real coordinates, therefore, no graph can be drawn through this point. Now Substituting, x = ( 0 ), we get y = f(0) = A√(0) = A(0)= 0. So the Second Point has Coordinates (0,0). And Substituting x = ( 1 ) we get y = f(1) = A√(1) = A(1) = A. So the Third Point has Coordinates (1,A). Since the first Point had coordinates that were not real, we now look for a fourth Point and choose x =(2). Now substitute x =(2) into y =f(2) = A√(2) = A(1.41)= 1.41A . So the fourth Point has coordinates (2,1.41A). We now Sketch the Curve through these Three Points. Please Click on the Image for a better view.

Given the Equation y = f(x) = A√x + B, where B is any Real Number, the Graph of this Equation would Translate Vertically ( B ) units. If ( B ) is a Positive Number, the Graph will move up ( B ) units, and if ( B ) is a Negative Number, the Graph will move down ( B ) units. To Sketch The Graphs of this Equation, We follow the Instructions and use the same values of ' x ' of Step #3. Please Click on the Image to get a better view.

Given the Equation y = f(x) = A√(x - B) where A and B are any Real Numbers, and ( A ) not equal to Zero ( 0 ), and x ≥ B. The Graph of this Equation would Translate Horizontally ( B ) units. If ( B ) is a Positive Number, the Graph will move to the Right ( B ) units and if ( B ) is a Negative Number, the Graph will move to the Left ( B ) units. To Sketch The Graphs of this Equation, we First set the Expression,' x - B ', that is under the radical sign Greater than or Equal to Zero, and solve for ' x '. That is,... x - B ≥ 0, then x ≥ B.

We will now use the following Three Values for ' x ', x = (B), x = ( B + 1 ) and x = ( B + 2 ) . We substitute each value of ' x ' into the Equation,... y = f(x) = A√(x - B)and get the respective corresponding value for each ' y '.

Given y = f(x) = A√(x - B), where A and B are Real Numbers, and ( A ) not equal to Zero ( o ) where x ≥ B. Substituting, x = (B) into the Equation we get y = f(B) = A√(B-B) = A√(0) = A(0) = 0. So the First Point has Coordinates (B,0). Now Substituting, x = ( B + 1 ), we get y = f(B + 1) = A√(B + 1 - B) = A√1 = A(1) = A. So the Second Point has Coordinates (B+1,A),and Substituting x = ( B + 2 )we get y = f(B+2) = A√( B+2-B) = A√(2) =A(1.41) = 1.41A. So the Third Point has coordinates (B+2,1.41A). We now Sketch the Curve through these Three Points. Please Click on the Image for a better view.

Given y = f(x) = A√(x - B) + C, where A, B, C are Real Numbers and ( A )not equal to Zero ( 0 ) and x ≥ B. If C is a Positive Number then the Graph in STEP #7 Will Translate Vertically ( C ) units. If ( C ) is a Positive Number, the Graph will move up ( C ) units, and if ( C ) is a Negative Number, the Graph will move down ( C ) units. To Sketch The Graphs of this Equation, We follow the Instructions and use the same values of ' x ' of Step #7. Please Click on the Image to get a better view.

Things Needed

Paper

Pencil and

Graph Paper

About the Author

Zadock Reid began writing professionally in 2008, with work appearing on eHow and several other websites. He is listed in "Who's Who Among America's Teachers." He holds a Bachelor of Arts in history from Andrews University in Michigan, a Master of Science in mathematics from the University of Illinois-Chicago and a Ph.D. in mathematics from Sussex College in Sussex, England.